## What is 'Uncovered Interest Rate Parity (UIP)'

Uncovered interest rate parity (UIP) is a proposition stating that the expected return on an uncovered, or unhedged, risk-free foreign currency investment should equal the return on a comparable domestic currency investment. When this relationship holds, the difference in interest rates between two countries will equal the relative change in currency foreign exchange rates over the same period. If the uncovered interest rate parity relationship does not hold, then there is an opportunity to make a risk-free profit using currency arbitrage or Forex arbitrage - Forex.

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## BREAKING DOWN 'Uncovered Interest Rate Parity (UIP)'

Uncovered interest rate parity (UIP) conditions consist of two return streams, one from the foreign money market interest rate on the investment and one from the change in the foreign currency spot rate. Said another way, uncovered interest rate parity assumes foreign exchange equilibrium, thus implying that the expected return of a domestic asset (i.e., a risk-free rate like a U.S. Treasury Bill or T-Bill) will equal the expected return of a foreign asset after adjusting for the change in foreign currency exchange spot rates.

There are two types of interest rate parity: covered interest rate parity and uncovered interest rate parity. When uncovered interest rate parity holds, there can be no excess return earned from simultaneously going long a higher-yielding currency investment and shorting a different lower-yielding currency investment or interest rate spread. Uncovered interest rate parity assumes that the country with the higher interest rate or risk-free money market yield will experience a depreciation in their domestic currency relative to the foreign currency.

## Uncovered Interest Rate Parity Formula and Example

When UIP holds the following relationship exists:

%Change in Expected Future Spot Price S(f)/S(d) = i(f) - i(d)

This equation shows that the expected change in the future spot foreign exchange rate over the same investment period should be equal to the difference in interest rates.

Where:

S(d) = Domestic Country Expected Future Spot Price

S(f) = Foreign Country Expected Future Spot Price

i(f) = Risk-free Foreign Interest Rate

i(d) = Risk-free Domestic Interest Rate

The return on an uncovered foreign-currency risk-free investment is represented by the following equation:

(1 + i(f))(1 - %Change in Expected Future Spot Price S(f)/S(d) - 1

The Total Return is dependent on the future change in the expected future spot rate and can be approximated as:

i(f) ~= %Change in Expected Future Spot Price S(f)/S(d)

## Empirically Analyzing Uncovered Interest Parity

There is only limited evidence to support UIP, but economists, academics and analysts still use it as theory and conceptual framework to represent rational expectation models. UIP requires the assumption that capital markets are efficient. Empirical evidence has shown that over the short- and medium-term time periods, the level of depreciation of the higher-yielding currency is less than the implications of uncovered interest rate parity. Many times, the higher-yielding currency has strengthened instead of weakened.

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